摘要：(西南师大附中高2009级第三次月考)已知圆C经过P.Q两点.且在y轴上截得的线段长为.半径小于5． (1)求直线PQ与圆C的方程． (2)若直线l∥PQ.且l与圆C交于点A.B..求直线l的方程． 解:(1) PQ为···························································· 2分 C在PQ的中垂线即y = x – 1上································ 3分 设C(n.n – 1).则······································· 4分 由题意.有······································································· 5分 ∴ ∴ n = 1或5.r 2 = 13或37(舍)······················ 7分 ∴圆C为············································································· 8分 解法二: 设所求圆的方程为 由已知得解得 当时.,当时.(舍) ∴ 所求圆的方程为 (2) 设l为···················································································· 9分 由.得································ 10分 设A(x1.y1).B(x2.y2).则················ 11分 ∵ . ∴ ···················································· 12分 ∴ ∴ ∴ m = 3或 – 4(均满足) ∴ l为···························································· 14分

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